Transport in ‘transport-optimized’ stellarators at low collision frequencies has been studied using a numerical method of solution of the bounce-averaged Fokker–Planck equation which describes both ripple-trapped and non-ripple-trapped particles in a stellarator. Diffusion rates in ‘transport-optimized’ stellarators had not previously been calculated at collision frequencies which are low enough for the effects of a radial electric field to be important. It was found that the configurations which were optimized for transport at the highest collision frequencies at which ripple-trapped particles exist give improved transport at all lower collision frequencies of interest, and also at higher collision frequencies. Standard stellarators have also been studied since in these cases the results can be compared with existing analytic theories and the transport mechanisms have been clarified as a result. Comparisons with Monte Carlo calculations show excellent agreement, and, although existing analytic methods of solution can strictly only be applied in rather few cases, some extensions of analytic results are discussed which enable us to explain quantitatively the behaviour observed.